We give a fresh introduction to the Khovanov Homology theory for knots and links, with
special emphasis on its extension to tangles, cobordisms and 2–knots. By staying within a …

Fixing the functoriality of Khovanov homology Page 1 Geometry & Topology 13 (2009) 1499–1582
1499 Fixing the functoriality of Khovanov homology DAVID CLARK SCOTT MORRISON KEVIN …

Abstract In [Duke Math. J. 101 (1999) 359–426], Mikhail Khovanov constructed a homology
theory for oriented links, whose graded Euler characteristic is the Jones polynomial. He also …

We propose a framework for unifying the sl (N) Khovanov–Rozansky homology (for all N)
with the knot Floer homology. We argue that this unification should be accomplished by a …

Mikhail Khovanov defined, for a diagram of an oriented classical link, a collection of groups
labelled by pairs of integers. These groups were constructed as homology groups of certain …

Using derived categories of equivariant coherent sheaves, we construct a categorification of
the tangle calculus associated to sl (2) and its standard representation. Our construction is …

The book is the first systematic research completely devoted to a comprehensive study of
virtual knots and classical knots as its integral part. The book is self-contained and contains …

arXiv:math/0504045v1 [math.GT] 3 Apr 2005 Page 1 arXiv:math/0504045v1 [math.GT] 3 Apr
2005 Fields Institute Communications Volume 00, 0000 Knot Polynomials and Knot Homologies …

Quasi-alternating links are a natural generalization of alternating links. In this paper, we
show that quasi-alternating links are" homologically thin" for both Khovanov homology and …

Over the last fifteen years, the face of knot theory has changed due to various new theories
and invariants coming from physics, topology, combinatorics and alge-bra. It suffices to …